Are perfect and imperfect information games modelled as fully and partially observable environments, respectively?
There is indeed a close parallel here, but the concepts are distinct. Every perfect information game is fully observable, but not every fully observable game is a game of perfect information.

A game of imperfect information is one in which you lack knowledge of any of the following:


The state of the game (e.g. current market prices).
The rewards you will receive from various states (i.e. utility and cost functions).


In contrast, in partially observable process (specifically, a POMDP), the requirement is that you must not know which state you are in.

This is a subtle distinction, so here are some examples:


A multi-armed bandit game with stationary distributions. Here, you know which state you are in (in fact, if the distributions are stationary, you know that the state doesn't change, except for the value of your winnings). You are not in a POMDP (the game is fully observable), but you are operating with imperfect information, because you don't know the utility function associated with different actions. You are operating in a regular MDP.
The game of chess has perfect information, and is also thus fully observable.
The game of poker has imperfect information because you cannot observe the current state of the game (you can't see the cards in your opponent's hand). It is thus a POMDP.